David Mumford

Archive for Reprints, Notes, Talks, and Blog

Professor Emeritus
Brown and Harvard Universities

skip to content

Work on Moduli and Geometric Invariant Theory (except Abelian Varieties)

Moduli spaces are essentially maps. In an ordinary map, a point on a piece of paper corresponds to a location on the earth. Similarly, a point in a moduli space corresponds to an object of some kind, a variety or bundle or something more elaborate. The set of all these objects is thus put together in this fine but rather intangible 'map' known as a moduli space. That's why I have put a map of part of Maine in the background.

  • An Elementary theorem in Geometric Invariant Theory, Bull. Amer. Math. Soc., 1961, pp. 483-487. Scanned reprint and DASH reprint
  • Topics in the Theory of Moduli, (published in Japanese), Sugaku , 1963. Scanned English manuscript
  • Projective Invariants of Projective Structures, International Congress of Mathematicians, Stockholm 1962, 1963, pp. 526-530. Scanned reprint
  • The Boundary of Moduli Schemes, mimeographed notes from the 1964 Woods Hole Symposium on Algebraic Geometry. Scanned manuscript
  • Picard Groups of Moduli Problems, in Arithmetic Algebraic Geometry, (Proceedings of a Conference in Purdue, 1963), Harper and Row, 1965. Scanned reprint
  • Two Fundamental Theorem on Deformations of Polarized Varieties (with T. Matsusaka), Amer. J. of Math., 1964, pp. 668-684. Scanned reprint and DASH reprint
  • Cover of the book Geometric Invariant Theory, Springer-Verlag, 1965; 2nd enlarged edition, (with John Fogarty), 1982; 3rd enlarged edition, (with Frances Kirwan and John Fogarty), 1994, DejaVu
  • Abelian Quotients of the Teichmuller Modular Group, Journal d'Analyse, 1967, 28, pp. 227-244. Scanned reprint
  • Periods of Moduli Spaces of Bundles on Curves (with P. Newstead), Amer. J. of Math., 1968, 90, pp. 1200-1208. Scanned reprint and DASH reprint
  • The Irreducibility of the Space of Curves of Given Genus (with P. Deligne), Publ. Math. de l'I.H.E.S., 1969, 36, pp. 75-109. Scanned reprint and DASH reprint
  • A Remark on Mahler's Compactness Theorem, Proc. Amer. Math. Soc., 1971, 28, pp. 289-194. Scanned reprint and DASH reprint
  • The Structure of the Moduli Spaces of Curves and Abelian Varieties, Actes du Congress Int. du Math., Nice, 1970; Gauthier-Villars, 1971. Scanned reprint
  • Introduction to the Theory of Moduli (with K. Suominen), in Algebraic Geometry, Oslo 1970 F. Oort editor, Wolters-Noordhoff, 1972, pp. 171-222.Scanned reprint
  • Matsusaka's Big Theorem (with D. Lieberman), in Algebraic Geometry, Arcata 1974, AMS Proc. of Symposia in Pure Math., 29, 1975, pp. 513-530. Scanned reprint
  • The projectivity of the moduli space of stable curves, I: Preliminaries on "det" and "Div" (with F. Knudsen), Math. Scand., 39, 1976, pp.19-55.
    The projectivity of the moduli space of stable curves, II: the stacks Mg,n (sequel by F. Knudsen), Math. Scand., 52, 1983, pp.161-199.
    The projectivity of the moduli space of stable curves III: the line bundles on Mg,n and a proof of trhe projectivity of the completion of Mg,n in characteristic 0 (sequel by F. Knudsen), Math. Scand., 52, 1983, pp.200-212. Scanned reprint
  • Stability of Projective Varieties, Monographie No. 24 de L'Enseignement Math., 23, 1977, pp. 39-110. Scanned reprint
  • On the Kodaira Dimension of the Moduli Space of Curves (with Joe Harris and an appendix by William Fulton), Inv. Math., 1982, pp.23-88. Scanned reprint and DASH reprint
  • Towards an Enumerative Geometry of Moduli Space of Curves, in Arithmetic and Geometry, edited by M. Artin, J. Tate, Birkhauser-Boston, 1983, pp.271-326. Scanned reprint
  • A Stratification of the Null Cone via the Moment Map (with Linda Ness), Amer. J. of Math., 106, 1984, pp.1281-1329. Scanned reprint and DASH reprint